Question

Consider a game in which a red die and a blue die are rolled. Let xR denote the value showing on the uppermost face of the red die, and define xB similarly for the blue die. (a) The probability distribution of xR is as follows. xR p(xR) 1 1/6 2 1/6 3 1/6 4 1/6 5 1/6 6 1/6

Find the mean, variance, and standard deviation of xR. (Round your answers to three decimal places.)

Mean = Variance = Standard deviation =

(b) What are the values of the mean, variance, and standard deviation of xB? You should be able to answer this question without doing any additional calculations. (Round your answers to three decimal places.) Mean = Variance = Standard deviation =

(c) Suppose that you are offered a choice of the following two games. Game 1: Costs $7 to play, and you win y1 dollars, where y1 = xR + xB. Game 2: Doesn't cost anything to play initially, but you "win" 2y2 dollars, where y2 = xR - xB. If y2 is negative, you must pay that amount; if it is positive, you receive that amount. For Game 1, the net amount won in a game is w1 = y1 - 7 = xR + xB - 7. What are the mean and standard deviation of w1? (Round your answers to three decimal places.) Mean = Standard deviation = (d)

For Game 2, the net amount won in a game is w2 = 2y2 = 2(xR - xB). What are the mean and standard deviation of w2? (Round your answers to three decimal places.) Mean = Standard deviation = (e)

Based on your answers to Parts (c) and (d), which game would you choose if you are quite a risky person? Game 2 Game 1

Answer #1

A game of chance involves rolling a standard, six-sided die. The
amount of money the player wins depends on the result of the die
roll:
* If the result is 1 or 2, the player wins
nothing;
* If the result is 3, 4, or 5, the player wins 8
dollars;
* If the result is 6, the player wins 42
dollars.
(Note: Your answer to the question below should be rounded to
three decimal places.)
If you play this...

PROBLEM #2
Suppose you play a game in which a fair 6 sided die is rolled
once. If the outcome of the roll (the number of dots on the side
facing upward) is less than or equal to 4, you are paid as many
dollars as the number you have rolled. Otherwise, you lose as many
dollars as the number you have rolled.
Let X be the profit from the game (or the amount of money won or
lost per...

On three rolls of a single die, you will lose
$14
if a
6
turns up at least once, and you will win
$6
otherwise. What is the expected value of the game?
Let X be the random variable for the amount won on a single play
of this game.
E(X)equals=____
dollars (Type an integer or a decimal rounded to the nearest
cent as needed.)

My friend and I are playing a gambling game in which we each
roll a die. We then compare the numbers on the two dice to
determine the outcome. If my roll is larger, I win $1 and my friend
loses $1. If her roll is larger, I lose $1 and she wins $1. And if
our two rolls are equal, we both don’t win or lose any money.
(a) Write your answers as simplified fractions: What is the
chance...

A spinner game has a wheel with the numbers 1 through 30 marked
in equally spaced slots. You pay $1 to play the game. You pick a
number from 1 to 30. If the spinner lands on your number, you win
$25. Otherwise, you win nothing. Find the expected net winnings for
this game. (Round your answer to two decimal places.)
A game costs $1 to play. A fair 5-sided die is rolled. If you
roll an even number, you...

Consider the following card game with a well-shuffled deck of
cards. If you draw a red card, you don't win. If you get a space
you win $1. If you draw a club, you win $3, if you draw the ace of
clubs you win $30.
a. Create a probability model for the amount you win at this
game.
b. Find the expected value for winning a single
game.
c. Find the standard deviation of the winnings.
d. Now suppose...

Suppose that the New England Colonials baseball team is equally
likely to win a game as not to win it. If 5 Colonials games are
chosen at random, what is the probability that exactly 3 of those
games are won by the Colonials? Round your response to at least
three decimal places.

The probability that someone will win a certain game is p = 0.67
p=0.67 . Let x x be the random variable that represents the number
of wins in 1286 1286 attempts at this game. Assume that the
outcomes of all games are independent. What is the mean number of
wins when someone plays the game 1286 times? (Round your answer to
1 place after the decimal point, if necessary.) μ μ = What is the
standard deviation for the...

The probability that someone will win a certain game is p = 0.37
p=0.37 . Let x x be the random variable that represents the number
of wins in 655 655 attempts at this game. Assume that the outcomes
of all games are independent. What is the mean number of wins when
someone plays the game 655 times? (Round your answer to 1 place
after the decimal point, if necessary.) μ μ = What is the standard
deviation for the...

In the game of roulette, a wheel consists of 38 slots numbered
0, 00, 1, 2,..., 36. To play the game, a metal ball is spun
around the wheel and is allowed to fall into one of the numbered
slots. If the number of the slot the ball falls into matches the
number you selected, you win $35; otherwise you lose $1.
Complete parts (a) through (g) below. (c) Suppose that you play
the game 100 times so that n=...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 16 minutes ago

asked 52 minutes ago

asked 58 minutes ago

asked 58 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago